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Newton's Third Law of Motion
A Brief History: Sir Isaac Newton '''Born:''' December 25, 1642 in Lincolnshire, England '''Died:''' March 31, 1727 in Kensington, London '''Sir Isaac Newton''' was one of the greatest and most influential English mathematicians and scientists of his time. He laid the foundation for differential and integral calculus. His work on optics and gravitation made him one of the greatest scientists in the world. Furthermore, his three laws of motion helped advance the study of physics to what we know today. Introduction: Isaac Newton's Second Law of Motion In order to understand Isaac Newton's Second Law of Motion, you must know the basic principles of '''Force'''. Once the fundamental rules have been established, you will be able to grasp his Second Law of Motion. Force is defined as a push or a pull in a given direction. Since a force has both magnitude (the "strength" of the force) and direction, it is a vector quantity. The SI unit for force is represented by the letter '''F'''. Measuring Forces Using Hooke's Law You may wonder-how do you measure a force? This can be answered quite simply: by using Hooke's Law. We can measure the magnitude of a force by recognizing that an applied force will stretch or compress a spring. Knowing that this was true, an English scientist named Robert Hooke was able to show that the magnitude of a force ('''F''') is directly proportional to the stretch or compression of a spring ('''x''') within certain limits. Hooke's Law is defined by: '''F''' = ('''k''')('''x''') Under the SI system of measurement, '''x''' is measured in meters ('''m''') and '''F''' is measured in Newton’s ('''N'''). One Newton is equal to about 1/4 pound of force or '''One Newton''' = '''1kg''' x '''m/s^2'''. The constant of proportionality, '''k''', is known as the spring constant. Its unit is the Newton per meter ('''N/m'''), and it is related to the spring stiffness; the greater the constant, the stiffer the spring. General Idea of Newton's Second Law Newton's Second Law of Motion can be stated as follows: The acceleration of an object produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. In terms of an equation, the net force is equated to the product of the mass multiplied by the acceleration. '''F'''('''net''') = '''m''' x '''a''' The above equation can be interpreted as: '''N''' = '''kg''' x '''m/s^2''' = ('''kg x m''')/'''s^2''' The Concept of the ''Law of Nature'' We know that Newton's First Law of Motion predicts the behavior of objects for which all existing forces are balanced. The first law states that if the forces acting upon an object are balanced, then the acceleration of that object will be: '''0 m/s^2''' or '''0 m/s/s'''. Objects at equilibrium (the condition in which all forces balance) will not accelerate. According to Newton, an object will only accelerate if there is a net or unbalanced force acting upon it. The presence of an unbalanced force will accelerate an object by changing either its speed, its direction, or both. With this knowledge, we can thus explore Newton's Second Law or the "Law of Nature". Newton's second law pertains to the behavior of objects for which all existing forces are not balanced. It states that the acceleration of an object is dependent upon two the net force acting upon the object and the mass of the object. The acceleration of an object (or the rate at which an object changes its velocity) depends directly upon the net force (also defined as the unbalanced force: '''F'''('''net''')) acting upon the object, and inversely upon the mass of the object. Therefore, the acceleration is directly proportional to the net force. The net force is the vector sum of all the forces. If all the individual forces acting upon an object are known, then the net force can be determined. A Helpful Way to Remember '''F'''('''net''') = '''m''' x '''a''' '''F'''('''net''') = '''m''' x '''a''' is a great example of how a variation in one quantity might effect another quantity. Whatever ''change'' is made of the net force, the same ''change'' will occur with the acceleration. For instance if the net force doubles, triples or quadruples, the acceleration will do the same. Likewise, whatever ''change'' is made of the mass, the opposite or inverse ''change'' will occur with the acceleration. If you double, triple or quadruple the mass, then the acceleration will be one-half, one-third or one-fourth its original value. In conclusion, Newton's second law provides the explanation for the behavior of objects under unbalanced forces. The law states that unbalanced forces cause objects to accelerate with an acceleration which is directly proportional to the net force and inversely proportional to the mass. A Brief Summary Newton's second law of motion explains how an object will change velocity if it is pushed or pulled upon. 1. If you do place a force on an object, it will accelerate. For example if change its velocity, and it will change its velocity in the direction of the force. 2. Acceleration is directly proportional to the force. For example, if you are pushing on an object, causing it to accelerate, and then you push the object twice as hard, the acceleration will be two times greater. 3. Acceleration is inversely proportional to the mass of the object. For example, if you are pushing equally on two objects, and one of the objects has five times more mass than the other, it will accelerate at one fifth the acceleration of the other. Normal Force, Frictional Force, and the Coefficient of Kinetic Friction In physics, there are three types of forces: Normal Force, Frictional Force, and the Coefficient of Kinetic Friction. Term Definitions and Explanations '''Normal Force (N):''' When an object is at rest on a horizontal surface (a desk for instance), it has weight, but it is ''not'' accelerating. For this reason, the weight of the object is not an unbalanced force...it is zero! Thus, another force must be present on the object to balance the effects of gravity. Since this second force is perpendicular to both the object and the surface it is called a '''normal force'''. The equation is as follows: '''F'''('''gravity''') = '''m''' x '''g''' '''Force of Friction F(f):''' Consider the following situation: A 5.0 kg object is pulled across a floor with an applied force of 20. Newton’s. The acceleration of the object is measured to be 3.0 m/s^2. This situation is illustrated in the diagram below: Something just doesn't seem right here: ''F'' doesn’t equal ''m'' times ''a''! However, since we know from Newton's second law that ''ma'' has to equal the unbalanced force ('''F'''net). In this situation, '''F'''net is equal to 15 Newton’s (5.0 kg x 3.0 m/s^2), ''not'' to the applied force of 20. Newton’s. You may wonder where the 5.0 Newton’s went. There is another force present here called: friction. '''Frictional forces''' are always present when two surfaces come into contact with each other. The direction of a frictional force on an object is always ''opposite'' to the direction of the object's motion. The symbol for '''frictional force''' is '''F(f)'''. Now we can complete the diagram by adding in the 5.0 Newton frictional force: The equation is as follows: '''F'''('''net''') = '''F'''('''applied''') - '''F'''('''friction''') '''Coefficient of Friction (μ):''' The coefficient of friction is one way of predicting how much friction will be produced on an object because of its contact with another surface. The frictional force of an object in motion is directly proportional to the normal force present on the object. that determines the amount of friction. This varies tremendously based on the surfaces in contact. There are no units for the coefficient of either static or kinetic friction. The equation is as follows: '''F'''('''friction''') = '''µ''' x '''F'''('''normal''') We can calculate µ by measuring the frictional force on an object and then dividing this value by the normal force present on the object. Examples: Practice Problems & Solutions References Resources